Wiener path integrals and the fundamental solution for the Heisenberg Laplacian

In this paper, we present an explicit calculation of the heat kernel, fundamental solution and Schwartz kernel of the resolvent for the Heisenberg Laplacian using Wiener path integrals and their realizations via the Trotter product formula. This also gives another derivation of mehler’s formula.     

Experimental 511 W Composite Nd：YAG Ceramic Laser

We demonstrate a 511 W laser diode pumped composite Nd：YAG ceramic laser. The optical pumping system is consisted of five laser diode stacked arrays arranged in a pentagonal shape around the ceramic rod whose size is φ6.35×144mm. When the pumping power is 1600 W, the cw laser output up to 511 W at 1064nm can be obtained with a linear piano-piano cavity, and the optical-to-optical efficiency is 31.9%. To our knowledge, this is the highest value of laser output by using a newly invented composite Nd：YAG ceramic rod as the gain medium.     

A modified Silver–Meal heuristic for dynamic lot sizing under incremental quantity discounts

This note presents a variation of the well-known Silver–Meal heuristic to deal with lot sizing under a combination of a known, but time-varying, demand pattern along with an incremental quantity discount structure. The heuristic is shown to perform very well on a set of experiments presented in a recent paper in this journal. Additional experiments are performed to further explore the time horizon effects on the relative performance of the newly proposed heuristic compared to the two best performing ones from the previous paper.     

A Crowning Moment for Wiener Indices

The Wiener (Sum of All Distances) Index for three out of the four classes of hexagonal models or regular planar hex-patterns used to model graphite and similar structures have been known for a few years. In this paper we find the Wiener Index for the Crown or Beehive hexagonal model.     

Optical characterization of CdTe/ZnSe fractional monolayer structures grown by atomic layer epitaxy

Luminescence properties of CdTe/ZnSe fractional monolayer grown by atomic layer epitaxy have been investigated. To investigate the origin of the highly efficient luminescence, various optical spectroscopic methods such as, photoluminescence (PL), temporal/spatial resolved PL, temperature dependence PL, and excitation power dependence PL have been used. It is found that structural inhomogeneities affect dominant influence on the line width and line shape of luminescence. The luminescence intensity greatly enhanced by the localization of exciton at the disorder induced localized states.     

Hochschild- and Cyclic-Homology of LCNT-Spaces

We define a class of topological spaces ( LCNT spaces ) which come together with a nuclear Fréchet algebra. Like the algebra of smooth functions on a manifold, this algebra carries the differential structure of the object. We compute the Hochschild homology of this algebra and show that it is isomorphic to the space of differential forms. This is a generalization of a result obtained by Alain Connes in the framework of smooth manifolds.     

A synthesis of assignment and heuristic solutions for vehicle routing with time windows

This paper proposes a three-stage method for the vehicle-routing problem with time window constraints (VRPTW). Using the Hungarian method the optimal customer matching for an assignment approximation of the VRPTW, which is a travel time-based relaxation that partially respects the time windows, is obtained. The assignment matching is transformed into feasible routes of the VRPTW via a simple decoupling heuristic. The best of these routes, in terms of travelling and vehicle waiting times, form part of the final solution, which is completed by the routes provided by heuristic methods applied to the remainder of the customers. The proposed approach is tested on a set of standard literature problems, and improves the results of the heuristic methods with respect to total travel time. Furthermore, it provides useful insights into the effect of employing optimal travel time solutions resulting from the assignment relaxation to derive partial route sets of the VRPTW.     

Decoherence within a single atom

An “almost diagonal” reduced density matrix (in coordinate representation) is usually a result of environment induced decherence and is considered the sign of classical behavior. We show that the proton of a ground state hydrogen atom can indeed possess such a density matrix. This example demonstrates that the “almost diagonal” structure may be derived from an interaction with a low number of degrees of freedom which play the role of the environment. We also show that decoherence effects in our example can only be observed if the interaction with the measuring device is significantly faster than the interaction with the environment (the electron). In the opposite case, when the interaction with the environment is significant during the measurement process, coherence is maintained. Finally, we propose a neutron scattering experiment on cold He atoms to observe decoherence which shows up as an additional positive contribution to the differential scattering cross section. This contribution is inversely proportional to the bombarding energy.